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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 6
# Folio 49r, page id 00068051:0097
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De Transcendentius differentundo Tollibilibus et quod si oneuggaatur; nn aeq. diferentiam omnia
queant postremo ad aeg. differeatiali cacoatem, quae debet
esse
a si quantilis st transcenieas
a pater et hinc rediici posse via ad unicam tatem Euusaepdent ( 30+ 3y  50+ 51Y rf9y = 0
dy. dx  10+ Ny +1299,. 20 + ay + 227y.
sit
LM +N = 0 si N = G VX fiet LN- des 
N = _(2) yiX fiet  a X Z y (3) g.X + dx (4) qX seu dy P+ dx Q = dy (X) + du N)
dy: dx = 628 A: B
porio iso
M C p set M lg L E log p Ergo M(d L 1L  sa B. B  pe)d P. L.
et
+L,  d L. jam d L = M. L dL + sol: L d
-
Ergo fiet dP M 
jam dL = dy () + ax (L) et aM = ay () + d dx (I). Ergo ex aegq. 2, 5, 67
(ettdus P = dx Z + M. L Rdy + M L Sdx 1 fdL et F dy + side. L. Wax
fiet 04 dy (N) + dx (N) + M L (L) du + M. L= (LDAx + (AL: L (M dy + saL: L (MD ax
0
et ex gert.fiec (V) + M. L = L) + (aL: L(M) A + (D + M. L= 1y + (a L: L (n D B = 
seu ma: L (A D
et fiet:  (L): L dy + (Di L ex (+ A(()) dy + A_, (X). D dx + (N) (2) dy + (N) () ax
m = = N: L. hic ob
L
1X
a = () ay +CY)
Ad (X) = (. (1).)dy +C
a(XD = (1 (ND)  (1
L((2))  (((1)3.) ayr VL. C1).
et ita seo rro
2 (L) dy rt) ax=
L
+ B(1(XD.) dyt B ((X B. I) ex + (X Y (B dy + (A B BD ex
FM. N( SA ((L).) dytA (C CL). B dx + (L) (1) dy +(1) (N) ax ( 2) A
CB(1((LD) dy +B(. ((+ D. ) ax =+ (L MB) dy (LAB) ax (()B
=G)A + (DB. L () L. M. (1) ay  L MYEX L LK (M) Ly t LN C M B dx
 = M N(L) dy= MN(LDdX
(N) AENDBOnNiEeB(A C Cn ).) dy + A C. C9). D ax + (M) () ay t B ) () dx
LB (1 (n).) dy +B ((. C n J. ) ax (1) () ay Xl) By ax
A (1) =+ B(CMY
Ex, hac 6qualione collendo dy. dx per cag. 1
ut prodeat aequad identica
debent oia talia esse
ler exhis patet suffecisse si statum ab initio ad solventam aequ. 1.
di ad hibuissemus non aryu. 2. sed aeg. I1 scrbendo (dL: L + SI=0
quia in arg. 1. nes in effectu eo redacta est reduci pe, posito
si, M, ( esse ordinarias, non ita et () (M) etc. sunt odinario
adeoque ora in ory. U demto (dL: L. Ergo abt aequatio quaesita,
solvi pt per aeq. quae sit saL: L + 61 =0. simplicarem
utique quam 2. et genegaliter, si differentremus aegu.
aaequadem 2. et differentialem conjungamus cum orqu. 1
datu, contrnuando semper demue rem o unicam trausien
dentalem resid ad aequadem reducemus in qua oes transce
dentales differentiando collibiles (nempe
sevales nempe sunt Tetragoniftdcae, vel Exptonen
tiales supersunt praeter unicam. ergo semper
res  reduci pb ad unicam Transcendentatem
sollibliem differentiando.
incisio, non esse posibile
 mitem
differentiates
Unde jam suspicari
2
sit omnes aquades
implicatae, seu tangentium inversae
per socas Tetragonistica vel Exponentiales colanti
Cogitandum ergo de genere novo exprimendi apto
saltem ad constructiones
edi
fratio